Could you please verify that you have set the correct Consumer Key / API Key and Consumer Secret / Secret Key for your application in JFBConnect > Configuration > LinkedIn (and that you're not using the OAuth User Token and Secret)?
No other users have been reporting any errors regarding login with LinkedIn, which leads me to believe it might be your LinkedIn application and something being configured incorrectly. I am aware that it is on the LinkedIn side, so after a quick Google search, other websites encountering the same error had used the incorrect api and secret keys. This is the reason why I suggested that as a first step for you to look at.
If those values were input correctly into JFBConnect configuration, could you take a screenshot of your application settings at developer.linkedin.com and attach them to a PM for me? You can find the PM envelope icon under my avatar and add the file by uploading, then hitting the green arrow to attach the file to the message.